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Zero group refractive index

  1. May 10, 2016 #1
    1. The problem statement, all variables and given/known data.
    I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency.

    2. Relevant equations.
    \frac{2\omega n L}{c} &= 2m\pi

    n_g &= n + \omega \frac{dn}{d\omega}

    3. The attempt at the solution.
    I have considered a uniform plane wave propagating within the cavity satisfying the following relation
    \frac{2\omega n L}{c} &= 2m\pi
    where ω is the angular frequency, n is the effective refractive index and L is the length of the laser cavity. I have derived the group refractive index as follows
    n_g &= n + \omega \frac{dn}{d\omega} \\
    &= \frac{c m \pi}{\omega L} - \frac{c m \pi}{ \omega L}\\
    &= 0

    If this is correct, I don't understand what this is physically entailing. Any insight would be much appreciated! Thank you.
  2. jcsd
  3. May 11, 2016 #2


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    Science Advisor
    Homework Helper

    You are calculating the group index of refraction for a monochromatic wave, which is of course zero.
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